G IMPERF
5. The law of diminishing marginal utility applies: as the rate of consumption increases, the marginal utility derived from consuming additional units of a good
will decline. Utility is a term economists use to describe the subjective personal benefits that result from taking an action. The law of ity states that the ~ i a r ~ ~ ~ a ~ (or additional) ~ tderived from consuming successive units of a ~ ~ ~ t ~ product will eventually decline as the rate of consumption increases. For example, the law says that even though you might like ice cream, your marginal satisfaction from additional ice cream will eventually decline as you eat more and more of it. Ice cream at lunchtime might be great. An additional helping for dinner might also be good. However, after you have had it for lunch and dinner, another serving as a midnight snack will be less attractive. When the law of diminishing marginal utility sets in, the additional utility derived from still more units of ice cream declines.
The law of diminishing marginal utility explains why, even if you really like a certain product, you will not spend your entire budget on it. As you increase your consumption of any good, including those that you like a lot, the utility you derive from each additional unit will become smaller and smaller and eventually it will be less than the cost of the unit.
At that point, you will not want to purchase any more units of the good.
The law of diminishing marginal utility helps us understand the law of demand and the shape of the demand curve. The height of an individual’s demand curve at any specific unit is equal to the maximum price the consumer would be willing to pay for that unit-
~~~~t to the consumer-given the number of units he or she has already purchased. Although marginal benefit is measured in dollars, the dollar amount reflects the opportunity cost of the unit in terms of other goods forgone. If a consumer is willing to pay, at most, $5 for an additional unit of the product, this indicates a willingness to give up, at most, $5 worth of other goods. Because a consumer’s willingness to pay for a unit of a good is directly related to the utility derived from consuming the unit, the law of diminishing marginal utility implies that a consumer’s marginal benefit, and thus the height of the demand curve, falls with the rate of consumption.
Exhibit 1 shows this relationship for a hypothetical consumer Jones, relative to her weekly consumption of frozen pizza. Because of the law of diminishing marginal utility, each additional pizza consumed per week will generate less marginal utility for Jones than the previous pizza. For this reason, Jones’s maximum willingness to pay-her marginal benefit-will fall as the quantity consumed increases. In addition, the steepness of Jones’s demand curve, or its responsiveness to a change in price-its elasticity-is a reflection of how rapidly Jones’s marginal utility diminishes with additional consumption. An individual’s demand curve for a good whose marginal value declines more rapidly will be steeper.
Given what we now know about a consumer’s maximum willingness to pay for addi- tional units of a good, we are now in a position to discuss the choice of how many units the consumer will choose to purchase at various prices. At any given price, consumers
Marginal Utility, Consumer Choice, and the Demand Curve of an hdividcrc’ 1 5 1
Diminishing M a r g i n a l Utility and the Individual’s Demand Curve
Quantity of frozen pizzas per week
An individual’s demand curve, Jones’s demand for frozen personal pizzas in this case, reflects the law of diminishing marginal utility. Because marginal utility ( M U ) falls with increased consumption, so does the consumer’s maximum willing- ness to pay-marginal benefit (MS). A consumer will purchase until Mi3 = Price, so at a price of $2.50 per pizza, Jones would purchase three pizzas and receive a consumer surplus shown by the shaded triangle.
will purchase all units of a good f o r which their maximum willingness to pay-their marginal benefit-is greater than the price. They will stop at the point where the next unit’s marginal benefit would be less than the price. Although there are some problems re- lated to dividing up certain kinds of goods (for example, it is hard to purchase half a car), we can generally say that a consumer will purchase all units of a good up to the point where the marginal benefit from it equals the price of the good ( M B = P).
Returning to Exhibit 1, if the price of frozen pizza were $2.50, Jones would purchase three frozen pizzas per week.4 Remember from Chapter 3 that consumer surplus is defined as the difference between the maximum price the consumer is willing to pay and the price actually paid. Jones’s maximum willingness to pay for the first unit is $3.50, which, at a price of $2.50, generates $1.00 of consumer surplus for Jones. When a consumer has purchased all units to the point where M B = iF: total consumer surplus is maximized. It is shown by the total triangular area under the demand curve that lies above the price. Total consumer surplus for Jones is shown as the shaded area in Exhibit 1.
Within this framework, how would a consumer respond to a decline in the price of a good? The consumer will increase purchases to the point where marginal benefit diminishes to the level of the new lower price. If marginal utility declines rapidly with consumption, the consumer will expand his or her purchases only slightly. If marginal utility declines less rapidly, it will take a larger expansion in purchases to reach this point.
If the price were to rise, the consumer would cut back on purchases, eliminating those for which marginal benefit were now less than the price. This link between marginal benefit and maximum willingness to pay is the basis for the law of diminishing marginal utility, which underlies a person’s demand curve for a product. The shape and steepness of the curve, for example, depends upon his or her marginal utility.
the second unit because MB > P For the third unit, MB = P so Jones would be indifferent to g it For a good that is easily divisible, say, pounds of roast beef, the consumer would continue Thus, economist? are comfortable with simply concluding thdt the consumer will purchase this I1 purchase three frozen pizzas
~~~
~ -
~~~~- ~
152 c H A P T E R 7 Consumer Choice and Elasticity
The last time you were at the mall, you probably saw something, perhaps a nice billfold, that you liked. After all, there are many things we would like-many different alternatives that would give us utility. Next, you looked at the price tag: “Fifty dollars, wow! That’s too much.” What you were really saying was, “I like the billfold, but not as much as the
$50 worth of other goods that I would have to give up for it.” Consumer choice is a constant comparison of value relative to price. Consider another example: perhaps you prefer steak to less costly hamburger. Even if you do, your happiness might be better served if you were to buy the hamburger and then spend the extra money you saved on something else.
The idea that consumers choose among products by comparing their relative marginal utility ( M U ) to price ( P ) can be expressed more precisely. A consumer with a limited amount of income to spend on a group of products is not likely to do the following math, but will act as though he or she had, and will end up with
MU* - M U , - - . . . - - - MUn
~~ -
PA P B p n
In this formula, MU represents the marginal utility derived from the last unit of a prod- uct, and P represents the price of the good. The subscripts
*,
B ,. .
., indicate the differ- ent products available to the consumer. This formula implies that the consumer will maximize his or her satisfaction (or total utility) by ensuring that the last dollar spent on each commodity yields an equal degree of marginal utility. Alternatively stated, the last unit of each commodity purchased should provide the same marginal utility per dollar spent on it. Thus, if the price of a gallon of ice cream is twice as high as the price of a liter of Coke, a consumer will purchase these items to the point where the marginal utility of the last gallon of ice cream is twice as high as the marginal utility of the last liter of Coke.Perhaps the best way to grasp this point is to think about what happens when your ra- tios of marginal utility to price are not equal for two goods. Suppose that you are at a local restaurant eating buffalo chicken wings and drinking Coke. For simplicity, assume that a large Coke and an order of wings each costs $2. With your $10 budget, you decide to purchase four orders of wings and one large Coke. When you finish your Coke, there are still lots of wings left. You have already eaten so many wings, though, that those remaining do not look as attractive. You could get more utility with fewer wings and another Coke, but it is too late. You have not spent your $10 in a way that gets you the most for your money. Instead of satisfying the above condition, you find that the marginal utility of wings is lower than the marginal utility of a Coke, and because they both have the same price ($2), this implies that
- $ Muwing?
<-
MU,,,Pwings PCoke
If you had purchased fewer wings and more Coke, your total utility would have been higher. Spending more on Coke would have lowered its marginal utility, decreasing the value of the right side of the equation. Simultaneously, spending less on wings would have raised the marginal utility of wings, increasing the value of the left side of the equation. You will maximize your utility-and get the most “bang for the buck” from your budget-when you make these values (the ratios) equal.
The equation can also be used to illustrate the law of demand. Beginning with a situation in which the two sides were equal, suppose that the price of wings increased. It would lower the value of MU/P for wings below the MU/P for Coke. In response, you would reallocate your budget, purchasing fewer of the more costly wings and more Coke.
Thus, we have the law of demand-as the price of wings rises, you will purchase less of them. When people try to spend their money in a way that gives them the greatest amount of satisfaction, the consumer decision-making theory outlined here is difficult to question.
In the next section, we will take the theory a little further.
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Marginal Utility, Consumer Choice, and the Demand Cirri e of an Indirtduo 153
The demand curve or schedule shows the amount of a product that consumers are will- ing to buy at alternative prices during a specific time period. The law of demand states that the amount of a product bought is inversely related to its price. We have seen how the law of demand can be derived from fundamental principles of consumer behavior.
Now, we go further and distinguish two different phenomena underlying a consumer’s re- sponse to a price change. First, as the price of a product declines, the lower opportunity cost will induce consumers to buy more of it-even if they have to give up other products.
This tendency to substitute a product that has become cheaper for goods that are now rela- tively more expensive is called the i t u t ~ ~ ~ effect of a price change.
Second, if a consumer’s mone ome is fixed, a reduction in the price of a product will increase his or her real income-the amount of goods and services he or she is able to purchase with that fixed amount of money income. If your rent were to decline by $100 per month, for example, that would allow you to buy more of a number of other goods.
This increase in your real income has the same effect as if the rent had remained the same but your income had risen by $100 per month. As a result, this second way in which a price change affects consumption is called the ~ ~ c o ~ e effect. Typically, consumers will respond to the income effect by buying more of the cheaper product and other products as well because they can better afford to do so. Substitution and income effects generally work in the same direction-in other words, in the same way; they both cause consumers to purchase more of a good as its price falls and less of a good as its price rises. (Both the income and substitution effects are derived graphically in the addendum to this chapter, ti- tled “Consumer Choice and Indifference Curves.”)
You may have heard the saying that “time is money.” It is certainly true that time has value and that this value can sometimes be measured in dollars. As we have learned, the mone- tary price of a good is not always a complete measure of its cost to the consumer. Con- suming most goods requires not only money, but time as well; and time, like money, is scarce to the consumer. So a lower time cost, like a lower money price, will make a prod- uct more attractive. For example, patients in a dentist’s office would prefer a shorter wait before receiving care. One study showed that dental patients are willing to pay more than
$5 per minute saved to shorten their time spent in waiting rooms.6 Similarly, commodities such as automatic dishwashers, prepared foods, air travel, and taxi service are demanded mainly for the time savings they offer. People are often willing to pay relatively high money prices for goods that help them save time.
Time costs, unlike money prices for goods, differ among individuals. They are higher for persons with higher wage rates, for example. Other things being equal, high-wage con- sumers choose fewer time-intensive (and more time-saving) commodities than people with lower time costs and wages. For example, high-wage consumers are overrepresented among airplane and taxicab passengers but underrepresented among television watchers, chess players, and long-distance bus travelers. Can you explain why? You can, if you un- derstand how both money and time costs influence the choices of consumers.
Failure to account for time costs can lead to bad decisions. For example, which is cheaper for consumers: (1) waiting in line three hours to purchase a $25 concert ticket or ( 2 ) buying the same ticket for $40 without standing in line? A consumer whose time is worth more than $5 per hour will find that $40 without the wait in line is less costly. As you can see, time costs matter. For example, when government-imposed price ceilings (discussed in Chapter 4) create shortages, rationing by waiting in line is frequently used.
For many consumers, the benefit of the lower price due to the ceiling will be largely, if not entirely, offset by their increased time cost of having to wait in line.
~~
’The substitution effect will always work in this direction. The income effect, however, may work in the reverse direction for some types of goods known as infenor goods. These will be addressed later in this chapter.
6Rexford E. Santerre and Stephen P. Neun, Health Economics: Theories, insights and Industry Studies (Orlando, Fla.: Harcourt, 2000) 113.
~ b s ~ i t ~ ~ i o n effect That part of an increase (decrease) in amount consumed that is the result of a good being cheaper (more expensive) in relation to other goods because of a reduction (increase) in price.
That part of an increase (de- crease) in amount consumed that is the result of the con- sumer’s real income being expanded (contracted) by a reduction (rise) in the price of a good.
just as individual demand curves do
Jones Smith
$3.5(
8
$2.51a ._ L
$3.50
8
$2 50-
La
1 3 2 3
Weekly frozen pizza consumption
Price e ~ a s ~ i c i ~ y of demand The percentage change in the quantity of a product de- manded divided by the per- centage change in the price that caused the change in quantity. The price elasticity of demand indicates how respon- sive consumers are to a change in a product's price.
The market demand schedule is the relationship between the market price of a good and the amount demanded by all the individuals in the market area. Because individual con- sumers purchase less at higher prices, the amount demanded in a market area as a total is also inversely related to price.
Exhibit 2 shows the relationship between individual demand and market demand for a hypothetical two-person market. The individual demand curves for both Jones and Smith are shown. Jones and Smith each consume three frozen pizzas per week at a price of
$2.50. The amount demanded in the two-person market is six pizzas. If the price rises to
$3.50 per pizza, the amount demanded in the market will fall to three pizzas, one de- manded by Jones and two by Smith. The market demand is simply the horizontal sum of the individual demand curves of consumers-in this case, Smith and Jones.
In the real world, however, there can be millions of consumers in a market. But the relationship between the demand curves of individuals and the market demand curve will still be just like the one shown in Exhibit 2. At any given price, the amount purchased in the market will be the sum of the amounts purchased by each consumer in the market. Fur- thermore, the total amount demanded in the market will decline as price increases because individual consumers will purchase fewer units at the higher prices. The market demand curve reflects the collective choices of the individual consumers.
Although it is important to recognize that consumers will buy less of a product as its price increases, for many purposes, it is also important to know whether the increase will lead to a large or small reduction in the amount purchased. Economists have designed a tool called the price elasticity of demand to measure this sensitivity of amount
purchased in response to a change in price. The equation for the rice e ~of ~ § ~ ~ ~ ~ ~ ~ demand is as follows:
Percentage change in quantity demanded - % B Q
Price elacticity of demand = -
Percentage change in price % B P
Elnstrcrti of Deinnnd 155 This ratio is often called the elasticity coefficient. To express it more briefly, we use the
notation %AQ to represent percentage change in quantity and %AP to represent percent- age change in price. (The Greek letter delta [ A ] means “change in.”) The law of demand states that an increase in a product’s price lowers the quantity of it purchased, whereas a decrease in price raises it. Because a change in price causes the quantity demanded to change in the opposite direction, the price elasticity coefficient is always negative, although economists often ignore the sign and use the absolute value of the coefficient.
To see how the concept of elasticity works, suppose that the price of the Ford Explorer rises 10 percent, while other prices remain the same. Ford could expect Explorer sales to fall substantially-perhaps 30 percent-as sport-utility vehicle (SUV) buyers respond by switching to other SUVs whose prices have not changed. This strong response by buyers means that the demand for the Explorer is elastic.
Now consider a different situation. Suppose that, because of a new tax, the price of not only the Explorer but o f a l l new SUVs rises 10 percent. In this case, consumers’
options are much more limited. They can’t simply switch to a cheaper close substitute as they could when the price of the Explorer alone rose. They might either simply pay the extra money for a new SUV or settle for a used SUV instead. Because of this, the 10 percent rise in the price of all new SUVs will lead to a smaller consumer response, perhaps a 5 percent decline in sales of new SUVs.
To calculate the elasticity coefficient for the Explorer in our example above, we begin with the 30 percent decline in quantity demanded and divide by the 10 percent rise in the price that caused the decline. Thus, the elasticity of demand for the Explorer would be:
= - 3
% AQuantity - - 30%
% APrice + l o %
-
(or 3.0 if we ignore the minus sign). This means that the percentage change in quantity demanded is three times the percentage change in price.
To calculate the demand elasticity for all SUVs (our second example), we see that the percentage change in quantity, 5 percent, divided by the percentage change in price, 10 percent, gives us-1/2, or -0.5. When it comes to the price elasticity of demand for all SUVs, the percentage change in quantity demanded (using our hypothetical numbers) is only half the percentage change in price, not three times the percentage change in price as it was with the Explorer.
Often, we will have to derive the percentage change in quantity and price. If you know the quantities that will be purchased at two different prices, you can then derive the percentage change in both the price and the quantity. For example, suppose that a price change from Po to P , causes a change in quantity demanded from Q, to Q,. The change in quantity demanded would therefore be Q, - Q,. To calculate the percentage change in quantity, we divide the actual change by the midpoint (or average) of the two quantities.’
Although it is often easy to find the midpoint without a formula (halfway between $4 and $6 is $5), it can also be found as (Q,
+
Q,)/2. Finally, because 0.05 is simply 5 percent, we mul- tiply by 100. Thus, we can express the percentage change in quantity demanded as:- x 100 ( Q o + Q i > / 2
Similarly, when the change in price is Po -
P,,
the percentage change in price isDividing the resulting percentage change in quantity by the percentage change in price gives us the elasticity.
..
3*
’This formula uses the average of the starting point and the ending point of the change so that it will give the same result whether we start from the lower or the higher price. This arc elasticity formula is not the only way to calculate elasticity, but it is the mo&t frequently used.